Repetitive controller design for track-following servo system of an optical disk drive

In the track-following servo system of an optical disk drive, external disturbances with significant periodic components cause tracking errors of a periodic nature. To effectively reject such disturbances, repetitive control has been employed. However, plant uncertainty makes it difficult to design a repetitive controller which both ensures system stability and improves tracking accuracy. In this paper, we examine the problem of repetitive controller design for an optical disk drive track-following servo system with norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition for robust stability of the repetitive control system is derived in terms of algebraic Ricatti inequality (ARI) or linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter. Through an experiment, it is verified that the designed repetitive controller has a remarkable performance to attenuate the periodic disturbance while preserving the overall stability.